Wednesday, September 5, 2018

Lesson 1-5: Drawing in Perspective (Day 15)

Today is my first day of subbing in the classroom. Of course, it's in the district where most of my subbing calls come from -- which is not the district whose calendar the blog follows. In the district where I sub today, this is only Day 7. But this blog follows the other district where it's Day 15, only because I find that calendar more suitable for Geometry pacing.

This is a middle school special ed class. I know that I've been going back and forth regarding whether I want to do "A Day in the Life" for each day that I sub. At first, I wrote that I only want "Day in the Life" when I sub in math classes, but on the other hand, I also want to do it for other middle school classes, since this is the level where I need to work on classroom management. Yet on the third hand, I don't necessarily want to do it for special ed classes -- especially if there's a special aide in the class who ends up running the entire class.

And that's exactly the case here. There is an aide who's worked at this school for 20 years, and so she knows all the insides and outs of this class. A second prospective aide is also present in the class, but of course it's the first aide who runs the class.

Thus I won't do "Day in the Life" today -- nor will I add the "subbing" label, since I've decided that I'll only label "Day in the Life" posts. I will write a little about my day today, just not in the "Day in the Life" format.

Like all middle schools in the district, the periods rotate. Even though today is Day 7, apparently it's the first day in this young school year that starts with sixth period. Apparently the first two days both started with Period 1, and then it was Period 2 on the third day, all the way until Period 6 today.

This teacher actually has sixth period conference. Afterwards there is more or less a self-contained class containing four seventh graders and three eighth graders, all male (but some are scheduled in other classes instead). The first three periods of the day are science, math, and history. Then fourth period is English 7, and fifth period is English 8. The boys go out to P.E. while the other grade is having English. Then since today is Wednesday, it's a Common Planning Day with a 1:30 dismissal.

In math class, the students complete a worksheet with 25 multiplication problems, each one of them being 2-digit by 1-digit. The worksheet isn't too difficult to find online:

https://www.math-drills.com/multiplication2/multiplication_0201_001.php

This reminds me of the Number Talk book that I purchased last week. I'm still haven't read the entire book yet -- and I hadn't quite reached Chapter 5 on multiplication by the time I subbed today. Thus as soon as I return home today I hastily read this chapter in order to blog about it here.

On one hand, maybe I should have brought the book with me knowing that I'd have special ed. On the other, it probably isn't a good idea to start doing Number Talks on a subbing day anyway. Author Ruth Parker tells us that it's better to start with dots (Chapter 2), not numbers, in order to reduce the students' anxiety. But today the students are assigned to multiply, so either I'd have to start Number Talks with multiplication or deviate from the teacher's lesson plan by talking about dots. Thus Number Talks are something that I should save for my own classroom, not subbing. Nonetheless, let's check out what Parker has to say about multiplication in her book.

Chapter 5 of Ruth Parker's Making Number Talks Matter is "Multiplication Across the Grades." Here is how it begins:

"In this chapter we focus on generalizable strategies for multiplication that are useful in helping students understand the properties of arithmetic and that provide a foundation for algebra."

Parker begins with 1-digit by 1-digit multiplication. She tells us that "timed tests" are a bad idea, since they're associated with math anxiety. Notice that traditionalists like to emphasize timed tests only because less time spent multiplying means more time for Algebra and Calculus. (In this case, it's difficult to classify my old "Dren Quizzes." They have the format of a traditional timed test, but I don't give the students a rigid time limit.) She writes:

"Early in our careers, we, too, were expected to use these [traditional] methods, but, knowing what we know now, we so wish we could have those students back again!"

She gives another analogy -- imagine flash cards with problems such as b * g = z. The letters on each card are arbitrary -- but that's what problems such as 2 * 7 = 14 look like to young children. It really reminds me of learning to multiply in different number bases -- and as we've seen, number base fans take lessons from both sides of the debate. (Like traditionalists, they know the importance of learning the times table in their chosen base, but in learning the table they use some of the tricks mentioned by Parker in this chapter.)

For example, Parker gives a Number Talk for the problem 7 * 8. (This problem doesn't come up in class today, but notice that 72 * 8 does.) Here are some methods that the students in her book are able to come up with:

Marta: I know that 7 times 7 is 49, so I added one more 7 and got 56.
Jacob: Well, 4 times 7 is 28, so if you add 28 and 28, that would be the same.
Teresa: 10 times 7 is 70, and you could take away two 7's or 14, and that's 56.

In today's class, I actually focus on the 8's rather than the 7's. I ask the students to find 5 * 8 first, and then add 8 twice more. Sometimes this works, but sometimes it doesn't -- for example, if students think that 5 * 8 is 45 rather than 40. I wonder whether Parker's 7's would be better than my 8's for this sort of problem.

Of course, all I'm doing is giving the students hints so they can figure out the answer. Once again, this isn't a true Number Talk where I ask students to find 7 * 8 or 72 * 8.

One of Parker's general strategies is "break a factor into addends." For a problem like 72 * 8, we would rewrite this as 70 * 8 + 2 * 8 = 560 + 16 = 576. Of course, this requires that the students already know what 7 * 8 is, to find 70 * 8.

Some of her strategies are even more inappropriate for this class. For example, in 72 * 8, we might notice that 72 = 9 * 8. Then 72 * 8 = 9 * 8 * 8 = 9 * 64. Then to find 9 * 64, we would notice that this is 10 * 64 - 64 = 640 - 64 = 576. This seems convoluted, but in fact Parker solves another problem (81 * 25) using this exact method.

Of course, Parker's methods are based on giving Number Talks the entire year, including some on subtraction (Chapter 4) and 1-digit multiplication before trying 72 * 8. I could never come into a classroom and try these methods directly. The best thing to do is just use the standard algorithm, but use Parker's tricks to find each intermediate product.

It's time for Geometry. This is what I wrote last year about today's lesson:

Lesson 1-5 of the U of Chicago text is called "Drawing in Perspective." In the modern edition of the text, perspective doesn't appear until Lesson 9-4. This is more logical, as Chapter 9 in both editions is the chapter on three-dimensional figures.

Perspective appeared as Lesson 0.8 in Michael Serra's Discovering Geometry, which we already covered nearly two weeks ago on Day 8. This time, I'll reblog the old Lesson 1-5 post from last year.

Indeed, Lesson 1-5 is the other worksheet I taught in middle school last year as part of my opening week activities. This is what I wrote about it:

Speaking of class, today I gave the last of the opening week activities previously posted on the blog -- Designing Buildings. This is what I wrote earlier about this activity:

And as it turns out, Nguyen covered something similar to this in her class as well:

http://fawnnguyen.com/designing-buildings/

Nguyen's lesson takes a different approach to drawing three-dimensional figures. For one, the focus on this lesson is on buildings. Her lesson begins by having some buildings already drawn and the students counting the "rooms" and "windows." (As it turns out, one "room" is one cubic unit of volume, and one "window" is one square unit of lateral area.)

I like the way that Nguyen's lesson begins. Unlike the bridge problem, where I wanted to avoid beginning the school year with a problem that's impossible to solve, here we begin with a very solvable problem. The only issue I have is with the second question, because it requires materials. I work from the assumption that most classrooms don't have the blocks and isometric dot paper that Nguyen's classroom has.

(As an aside, notice that cubes drawn on isometric dot paper are definitely not in perspective. This is because, while edges perpendicular on the cube intersect at 120 degrees on the iso dot paper, edges parallel on the cube remain parallel on the paper. Therefore there are no vanishing points.)

Then again, my worksheet is very similar to Nguyen's. On the front side, I gave the same example as she did and the three buildings for the students also come from the Ventura County teacher. I used two of her easier buildings -- A and B -- and the more challenging Building F.

The back side of my worksheet differs slightly from Nguyen's, though. Her worksheet specified the number of rooms and windows and asked the students to draw the buildings. Mine, on the other hand, simply has the students draw four different buildings with eight rooms and then asks them to count the number of windows in each one.

Now that I'm giving this activity in an actual classroom, I don't have any interlocking cubes (which I can only assume means "Lego bricks"), but I did find some small manipulative cubes. There weren't enough for me to give every group eight cubes (as specified in the assignment) -- instead I gave five to each group of sixth graders and seven to each group of seventh graders. (Half the seventh graders were absent because they hadn't satisfied California's 7th grade vaccination requirement.) The eighth grade groups did receive the full set of eight cubes. I believe that having actual blocks certainly helped the students visualize the three-dimensional buildings.

By the way, here are the rules the middle school classes came up with as part of the Rules Posters. At last I'm done discussing the rules here on the blog:

1. Raise your hand

2. Be silent and listen when it's someone else's turn to speak
3. Stay in your seat
4. Keep your hands to yourself
5. Keep the desks free of drawing
6. Treat the books, papers, and any other resources like you would treat your own items
7. Keep your voice at a conversational level
8. Allow the speaker to finish before you raise your hand
9. Speak in a respectful manner
10. Stay on task, work hard, and do your best!

Returning to 2018, let me end the cutting-and-pasting right here. Last year when I wrote this, I used this as an excuse to bring up classroom management from two years ago yet again. Now that subbing has started up again, my focus now isn't on past classrooms, but present and future classrooms.

Once again, today I don't think about classroom management because a very experienced aide is in charge of the class. There's no reason for me to focus on one of the seven New (School) Year's Resolutions today. Instead, I observe and think about what I'd do in this situation in my own class.

The only real management issue occurs in fifth period English 8. The aide assigns the students the following journal entry:

"What would you do if a friend was in serious trouble? How would you help them?"

There are only two eighth graders in the class (as the third, for some reason, isn't scheduled for this English class). Students are supposed to write three or four students in their journals and then discuss what they've written with the class. But one student writes the minimum, while the other writes barely a sentence. No discussion occurs, and both students just put on headphones and start watching non-academic YouTube videos on their Chromebooks.

How does the aide react to this? She simply doesn't give the eighth graders any participation points for this period. Apparently, this class has a participation points system with both positive and negative points. Each seventh grader earns five points today -- one each for science, math, and history, and two for the journal plus discussion. But each eighth grader earns only three points today.

Why, we might ask, do the eighth graders not complete the lesson? It's probably a combination of several factors. First, there are three seventh graders (the fourth goes home early today), and so a livelier discussion is possible than with just two eighth graders. For the seventh graders, this is just their second week on campus (as sixth grade is still elementary school in this district), and so they're more eager to talk to each other and make new friends -- while the eighth graders think that they own the school and don't have to work. Finally, this class is the only one after lunch and is thus the last class of the day. (The district came up with period rotations for exactly this reason!)

It's also worth noting that the guy with three sentences appears to have a headache and so he must go to the nurse. (During math time he uses Google calculator to finish only the bottom row of problems on his worksheet -- he does work hard on the rest of it.) The guy with one sentence has no excuse.

On one hand, simply not awarding the points means that the aide avoids argument. I don't have anything to say to the students, since anything I add would likely lead to argument. On the other hand, if students aren't going to work, I personally don't think they should be allowed to have any non-academic free time on the Chromebooks. But once they take the Chromebooks out, it's difficult to get them to avoid playing on them.

Only once does a student take out a cell phone today. Of course, it's the same eighth grader who writes only one sentence in his journal.

One thing I've been thinking about a possible future class of my own is what I should do about allowing phones and other electronics -- particularly those that are taken out after students claim that they're "done" with the assignment.

As of now, I think a good policy might be that phones are allowed only on test days -- and of course, that's after the student has completed the test. Then if students rush through the test just to get more phone time, their test grades will suffer -- as opposed to rushing through a mere assignment to get extra phone time (where the assignment is worth only a few points).

What should a student do who rushes through the assignment quickly? To me, the best answer would be nothing at all. Then if students know that the alternative is just to sit there bored doing nothing, then they might prefer slowing down and doing the assignment. Doing work for other classes might be a possibility -- but then what happens is students say "I need to use my phone/Chromebook to do research for my other classes," and then it quickly turns into non-academic playing on electronics.

Of course, I've already mentioned one other time when I would allow phones -- if a student is taking a math picture for me to post on a blog or Twitter. Thus, if a phone is out at the wrong time, then I'd require the student to send me an appropriate math photo immediately. If the appropriate math photo isn't received, then the student is punished for having phones out.

One thing I realize about today's classes is that I seem to establish more rapport with the seventh graders than the eighth graders. Part of this could be during history class. Three of the seventh graders are in this class, one eighth grader is at the nurse, and the other two aren't scheduled. And so I read the history book aloud with them, ending with a short preview of what they're to expect in seventh grade history. (In California, this is Medieval World History, with cultures from nearly every continent included in the curriculum.)

And so in hindsight, I wonder whether there's any way for me to connect to the eighth graders -- and perhaps I could have convinced them to work more on the journal assignment. I already know that it's wrong to compare this class to the seventh graders and say something like "They did the assignment, so why didn't you?" (The likely response would have been, "That's them, not us." As a rule, I should compare a class neither to myself nor to another class unless the comparison is favorable.)

But I could have casually brought up the seventh graders' responses, as well as discussed what my response to the question might be. Perhaps I could have engaged them in a conversation that's not directly related to the assignment and then drawn it back to the journals later on (especially with they guy who doesn't have a headache). This would be difficult, as I must come up with something to say before they put the headphones on. Once the headphones are on, they won't want to have any sort of conversation with me.

As far as other issues are concerned, only one student asks for a restroom pass today. It's the eighth grader who writes three sentences. It's the period after lunch -- but it's actually much closer to dismissal time than arrival time. The aide releases the students a few minutes early in order for them to make their special bus, and so it's reasonable to assume that he wants to use the restroom before boarding the bus. No other behavior issues appear today.

Once again, this class has both positive and negative participation points. Recently, I wrote about how negative points are a bad idea and can't replace real punishments. But again, I assume that if in this class, one student is very disruptive, the teacher will punish him more substantially than merely giving him a negative point.

Here is the worksheet for today:



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